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A346068
Numbers that are the product of distinct primes with prime subscripts raised to prime powers.
11
1, 9, 25, 27, 121, 125, 225, 243, 289, 675, 961, 1089, 1125, 1331, 1681, 2187, 2601, 3025, 3125, 3267, 3375, 3481, 4489, 4913, 6075, 6889, 7225, 7803, 8649, 11881, 11979, 15125, 15129, 16129, 24025, 24649, 25947, 27225, 28125, 29403, 29791, 30375, 31329, 32041, 33275, 34969
OFFSET
1,2
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = Product_{p in A006450} (1 + Sum_{q prime} 1/p^q) = 1.2271874... - Amiram Eldar, Jul 31 2021
EXAMPLE
675 = 3^3 * 5^2 = prime(prime(1))^prime(2) * prime(prime(2))^prime(1), therefore 675 is a term.
MATHEMATICA
Join[{1}, Select[Range[35000], AllTrue[Join[PrimePi[(t = Transpose @ FactorInteger[#])[[1]]], t[[2]]], PrimeQ] &]] (* Amiram Eldar, Jul 30 2021 *)
PROG
(Python)
from sympy import factorint, isprime, primepi
def ok(n):
f = factorint(n)
if not all(isprime(e) for e in f.values()): return False
return all(isprime(primepi(p)) for p in f)
print(list(filter(ok, range(35000)))) # Michael S. Branicky, Jul 30 2021
CROSSREFS
Intersection of A056166 and A076610.
Sequence in context: A068583 A074852 A322177 * A352519 A321874 A020252
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 30 2021
STATUS
approved